Problem: Ashley is 12 years younger than Stephanie. Stephanie and Ashley first met 3 years ago. Eight years ago, Stephanie was 3 times older than Ashley. How old is Stephanie now?
Explanation: We can use the given information to write down two equations that describe the ages of Stephanie and Ashley. Let Stephanie's current age be $s$ and Ashley's current age be $a$ The information in the first sentence can be expressed in the following equation: $s = a + 12$ Eight years ago, Stephanie was $s - 8$ years old, and Ashley was $a - 8$ years old. The information in the second sentence can be expressed in the following equation: $s - 8 = 3(a - 8)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $s$ , it might be easiest to solve our first equation for $a$ and substitute it into our second equation. Solving our first equation for $a$ , we get: $a = s - 12$ . Substituting this into our second equation, we get the equation: $s - 8 = 3($ $(s - 12)$ $ -$ $ 8)$ which combines the information about $s$ from both of our original equations. Simplifying the right side of this equation, we get: $s - 8 = 3s - 60$ Solving for $s$ , we get: $2 s = 52$ $s = 26$.